Lip Drooping - How Can I Fix Assymetry on my Lips

You may want to first see if this is correctable using botulinum toxin (ie., Dysport) in to the DAO muscle on that side. Alternatively a unilateral corner lift may be an option. SEE VIDEO BELOW

Asymmetry throughout the body is common. The key to fixing this is determining what the cause is.  In our case, the cause may be lack of support of the corner that is drooping, or increased muscle pull - either the same side is pulling it done, or the muscle on the other side is pulling it up.  If the problem is lack of support, then a filler can be placed to help it. This can be done in a way to only increase support, but not increase visible volume.  If the muscle is the problem, then carefully placed botox or dysport can help.

Obviously, you need a complete evaluation because pictures do not give all the answers. Keep in mind though, when dealing with asymmetries, it is usually possible to make things better, but it is difficult (some might even say "impossible") to make things perfect.